Heya, welcome to the Nascar section of this forum
Most of your questions will be answered by reading the sticky'd threads at the top of the page.
As far as being good on the track with a day a week or so, yeah - that's not problem at all. This will vary based on what your goals are, but the vast majority of the stuff you need to be good at on a velodrome can be practiced on a road bike or rollers. I know plenty of people who went all the way into the 2s on a day a week of velodrome practice or less.
So - read up on the stickies and then check back with us, eh? :-)